Question: Solve for $x$ and $y$ using substitution. ${-x+y = -3}$ ${x = 6y+8}$
Explanation: Since $x$ has already been solved for, substitute $6y+8$ for $x$ in the first equation. ${-}{(6y+8)}{+ y = -3}$ Simplify and solve for $y$ $-6y-8 + y = -3$ $-5y-8 = -3$ $-5y-8{+8} = -3{+8}$ $-5y = 5$ $\dfrac{-5y}{{-5}} = \dfrac{5}{{-5}}$ ${y = -1}$ Now that you know ${y = -1}$ , plug it back into $\thinspace {x = 6y+8}\thinspace$ to find $x$ ${x = 6}{(-1)}{ + 8}$ $x = -6 + 8$ ${x = 2}$ You can also plug ${y = -1}$ into $\thinspace {-x+y = -3}\thinspace$ and get the same answer for $x$ : ${-x + }{(-1)}{= -3}$ ${x = 2}$